论文标题
Kripke上下文，带有操作员和相应模态系统的双重布尔代数
Kripke Contexts, Double Boolean Algebras with Operators and Corresponding Modal Systems
论文作者
论文摘要
在本研究中统一了形式概念分析中背景和粗糙集理论中近似空间的概念，以定义kripke上下文。对于任何上下文（g，m，i），包括对象集的关系以及属性集的关系，给出了形式（（g，r），（m，s），i）的结构。 Kripke上下文基于基础背景的原始感受和半概念的集合产生复杂的代数。在抽象时，定义了带有操作员和拓扑DBA的双布尔代数（DBA）。这些代数的表示结果是根据适当的Kripke环境的复杂代数建立的。自然的下一步，制定了与这些代数类别相对应的逻辑。为上下文DBA提出了一个顺序的演算，其模态扩展为其与操作员和拓扑上下文DBA的上下文DBA提供逻辑。代数的表示定理导致这些逻辑的基于原始的语义。
The notion of a context in formal concept analysis and that of an approximation space in rough set theory are unified in this study to define a Kripke context. For any context (G,M,I), a relation on the set G of objects and a relation on the set M of properties are included, giving a structure of the form ((G,R), (M,S), I). A Kripke context gives rise to complex algebras based on the collections of protoconcepts and semiconcepts of the underlying context. On abstraction, double Boolean algebras (dBas) with operators and topological dBas are defined. Representation results for these algebras are established in terms of the complex algebras of an appropriate Kripke context. As a natural next step, logics corresponding to classes of these algebras are formulated. A sequent calculus is proposed for contextual dBas, modal extensions of which give logics for contextual dBas with operators and topological contextual dBas. The representation theorems for the algebras result in a protoconcept-based semantics for these logics.
